What is mathematics about?

I commend to you James Franklin’s latest article “Mathematics as a Science of Non‑abstract Reality: Aristotelian Realist Philosophies of Mathematics.”  It’s a helpful brief survey of different ways that an Aristotelian alternative to Platonist and nominalist approaches to mathematics might be developed.  (Franklin explores these issues in greater depth in his book An Aristotelian Realist Philosophy of Mathematics.) 

Frege on objectivity

It can be an interesting exercise every now and then to reread something that had a profound effect on you earlier in life.  In my case, Gottlob Frege’s grand 1918 essay “The Thought” is a piece that I find always repays renewed study.  I think I first read it almost 30 years ago, and it was one of several philosophical works on thought and language that began to break the hold on me of the metaphysical naturalism I had picked up as an undergraduate – though that was a slow process, taking a decade fully to unfold. 

Tennant on Aquinas’s Second Way

Every now and then I point out examples of professional academic philosophers badly misinterpreting some traditional argument for God’s existence, or mind-body dualism, or a natural law conclusion in ethics, or some other idea that is out of step with the naturalistic zeitgeist.  This is, I think, a useful exercise, because it shows how the conventional wisdom on these matters does not rest on actual knowledge or understanding of the ideas criticized.  It is instead held in place by errors and unexamined prejudices that mainstream academics who do not specialize in these matters tend to repeat back to one another and pass on to each new generation of graduate students, who then enter the profession and also repeat them back to each other and to their own students.  This has, over time, created a general assumption that “everyone knows” that the arguments are no good and not worth investigating further, even though a little effort would show that what “everyone knows” is demonstrably false.

Meta-abstraction in the physical and social sciences

One of the themes of Aristotle’s Revenge is the centrality of mathematical abstraction to modern scientific method, and the ways that it both affords modern physics tremendous predictive power but also, if we are not careful, is prone to generate philosophical fallacies and metaphysical illusions.  This is especially so where we are dealing with abstractions from abstractions – meta-abstractions, if you will. 

In his recent book on the philosophy of time, Raymond Tallis notes how this has happened in modern thinking about the nature of space and time.  First, physical space has come to be conflated with geometry.  Whereas the notions of a point, a line, a plane and the like were originally merely simplifying abstractions from concrete physical reality, the modern tendency has been to treat them as if they were the constituents of concrete physical reality.  But then a second stage of abstraction occurs when geometrical concepts are in turn conflated with values in a coordinate system.  Points are defined in terms of numbers, relations between points in terms of numerical intervals, length, width and depth in terms of axes originated from a point, and so on.  Time gets folded into the system by representing it with a further axis.  Creative mathematical manipulations of this doubly abstract system of representation are then taken to reveal surprising truths about the nature of the concrete space and time we actually live in.

Lacordaire on the existence of God

Preaching on theological topics is a tricky business.  The more substantive and rigorous a sermon, the greater the danger of its being inaccessible to the average listener.  But the more accessible it is, the greater the danger of its being woolly and banal.  (In our egalitarian and mawkish age, the latter vice is by far the more common one.  Indeed, I don’t think I’ve ever heard a sermon that exhibited the former vice.)   The 19^th-century Dominican theologian Henri-Dominique Lacordaire was famously able to strike the right balance.  Like other writers of the period, he has a style that to the contemporary reader is bound to seem a bit purple and prolix.  But, I think, he stops short of excess even on that score – indeed, the tone is, if anything, refreshing.  Whereas rhetorical excess in contemporary preaching tends to pull our attention downward, to our own petty sentimentalities, Lacordaire’s flourishes raise it up to God.

Aquinas on video

Many readers will be familiar already with the Thomistic Institute’s outstanding Aquinas 101 series of videos, which provide brief introductions to a wide variety of topics from Aquinas’s thought.  The Institute has now announced a new video series, Aquinas 101: Science and Faith, which will explore topics such as evolution, neuroscience, miracles, quantum mechanics, psychology, scientific method, reductionism, and the like.  The series begins on March 16, and the videos will be released weekly.  And on March 10, the trailer for the series will premiere and the Institute will host a live Q & A.

The Thomistic Institute also makes available a wide variety of other excellent video materials.  And while we’re on the subject, I should also call attention to a similar but different project, the superb iAquinas series of videos, which are in English, French, and Spanish.  Hours and hours of worthwhile viewing!

Preventive war and quarantining the healthy

A “preventive war” is a war undertaken proactively against a merely potential enemy, who has neither initiated hostilities nor shown any sign of intending imminently to do so.  The Japanese attack on the United States at Pearl Harbor is a famous example.  This is not to be confused with a “preemptive war,” which involves a proactive attack on an enemy who has shown signs of intending to initiate hostilities.  The Arab-Israeli Six-Day War is a standard example.

Smith and divine eternity

Quentin Smith, one of the most formidable of contemporary atheist philosophers, died late last year.  One of the reasons he was formidable is that he actually knew what he was talking about.  Most of his fellow atheist philosophers do not, as Smith himself lamented.  In his article “The Metaphilosophy of Naturalism,” Smith opined that “the great majority of naturalist philosophers have an unjustified belief that naturalism is true and an unjustified belief that theism (or supernaturalism) is false.”  He thought that most of them held their opinion as a prejudice, and didn’t know or engage with the most serious arguments of the other side.  If that is true even of most atheist philosophers, it is even more true of atheists outside of philosophy – other secularist academics, New Atheist propagandists, Reddit loudmouths, et al.

Tales from the links

An interview with philosopher William Simpson about Aristotle and quantum mechanics, at the Wolfson College Cambridge website.

Fr. John Naugle’s censored interview on the grave injustice of lockdowns.  Spiked on the damage that lockdowns have inflicted on the working class.  The BBC on the damage lockdowns have done to the education and mental health of children.  A new study finds that the more severe lockdowns have had no significant benefits.

At PREVIEWSworld, Grant Geissman discusses his gargantuan new book The History of EC Comics.  Mark Judge on EC Comics and the pulp takeover of American culture, at First Things.

Richard Marshall interviews philosopher Richard Swinburne at 3:16.

Can a Thomist reason to God a priori?

A priori knowledge, as modern philosophers use the term, is knowledge that can be gained independently of sensory experience.  Knowledge of mathematical and logical truths – 2 + 2 = 4, ~ (p • ~ p), etc. – provide the stock examples.  Anselm’s ontological argument contrasts with arguments like Aquinas’s Five Ways by trying to reason to God’s existence in a manner that is a priori in this sense.  Aquinas begins with empirical premises (about the reality of change, the existence of causal chains in nature, etc.) and reasons to God as the cause of the facts described in the premises.  Anselm’s argument, by contrast, begins with a definition of God as the greatest conceivable being and an axiom to the effect that what exists in reality is greater than what exists in thought alone, and reasons to God’s existence as the logical implication of these a priori premises. 

What is religion?

The question is notoriously controversial.  Consider a definition like the following, from Bernard Wuellner’s Dictionary of Scholastic Philosophy:

religion, n. 1. the sum of truths and duties binding man to God. 2. personal belief and worship in relation to God.  Religion includes creed, cult, and code.

By “creed,” what Wuellner has in mind is a system of doctrine.  A “cult,” in this context, has to do with a system of rituals of the kind associated with worship and the like.  The “code” referred to has to do with a system of moral principles.  So, the definition is telling us that doctrines, rituals, and moral principles are among the key elements of religion.

Princess Elisabeth of Bohemia on soul-body interaction

The letters exchanged between Descartes and Princess Elisabeth of Bohemia – especially their 1643 exchange on the interaction problem – are among the best-known correspondences in the history of philosophy.  And justly so, for they help to elucidate the true nature of that crucial problem and the inadequacy of Descartes’ response to it.  Though I think that in at least one important respect, Elisabeth errs in her characterization of the issue.

Koons on time and relative actuality

Rob Koons has reactivated his AnalyticThomist blog, which you must check out if you are interested in metaphysics done in a way that brings analytic philosophy and Thomism into conversation.  Rob was also recently interviewed on the What We Can’t Not Talk About podcast on the topic of Aristotle and modern science.  That topic is the focus of his recent work, and he has been especially interested in how Aristotelians ought to approach quantum mechanics and the nature of time. 

Narrative thinking and conspiracy theories

“Just because you're paranoid doesn't mean they aren't after you” is one of the most famous lines from Joseph Heller’s Catch-22.  I propose a corollary: Just because they’re after you doesn’t mean you’re not paranoid.

McGinn on the question of being

Colin McGinn is a philosopher whose work I always find interesting even when I disagree with it, which is often.  His book Philosophical Provocations: 55 Short Essays is made to be dipped into when one is in the mood for something substantive but not too heavy going.  And it is accurately titled, since on reading it I was indeed provoked – specifically, by the article on “The Question of Being.”

McGinn characterizes the issue as:

the question [of] …what it is for something to have being.  What does existence itself consist in – what is its nature?  When something exists, what exactly is true of it?  What kind of condition is existence?  How does an existent thing differ from a nonexistent thing? (p. 211)

The Gnostic heresy’s political successors

The Western world is the creation of the Church, and the crisis of the West is always at bottom the crisis of the Church.  This is especially so where the Church has receded into the background of the Western mind – where men’s plans are hatched in the name of progress, science, social justice, equity, or some other purportedly secular value, and make little or no reference to religion.  For liberalism, socialism, communism, scientism, progressivism, identity politics, globalism, and all the rest – this Hydra’s head of modernist projects, however ostensibly secular, is united by two features that are irreducibly theological.

Lawlessness begets lawlessness

As someone who is on record condemning lawlessness and sedition, I am appalled and horrified by what happened today in Washington, D.C.  It is indefensible and inexcusable, and the rioters and vandals ought to be prosecuted.  But then, the rioting and vandalism that occurred in Washington last summer – and in Minneapolis, Portland, Seattle, and other major cities – was also appalling, horrifying, indefensible, and inexcusable, and its instigators should have been prosecuted.  Yet some of the people who are now talking tough about law and order were then blathering on about “mostly peaceful protests,” “defunding the police,” and other such lunacy.  We are reaping what they sowed.  If you are going to tolerate and excuse left-wing political violence, you are opening the door to right-wing political violence.  But if you rightly condemn the latter, then to be consistent, you must condemn the former.  You must insist that all citizens respect law and order – your political allies no less than your political enemies.

Year-end open thread

Let’s bring this annus horribilis to an end with an open thread.  That annoyingly off-topic comment of yours I keep deleting?  It’s now on-topic, so bring it.  From Richard Rorty to Get Shorty, from Bend Sinister to Yes Minister, from Tanqueray to Ricky Jay… nothing now stands in your way.  Apart from basic blog etiquette, naturally.  Trolls are still kindly invited to get lost.  (Previous open threads archived here.)

The access problem for mathematical Platonism

Mathematical Platonism takes numbers and other mathematical objects to exist in a third realm distinct from the material and mental worlds, after the fashion of the Forms of Plato’s famous theory.  A common objection to this view, associated with philosophers like Paul Benacerraf, is epistemological.  In order for us to have knowledge of something, say these philosophers, we must be in causal contact with it.  But if numbers are abstract objects outside of space and time, then we cannot be in any such contact with them, because they would be causally inert and inaccessible to perception.  So, if Platonism were true, we couldn’t have knowledge of them.  Yet we do have such knowledge, which (the argument concludes) implies that Platonism is false.  This is known as the “access problem” for mathematical Platonism.

District Attorney Michel Foucault

In the diabolical new disorder of things metastasizing around us, churchmen subvert doctrine rather than teaching it, and public authorities subvert law and order rather than maintaining it.  To be sure, these cancers have been slowly spreading throughout the bodies ecclesiastical and politic for many decades.  What is new is the sudden ghastliness with which an aggressive heterodoxy and criminality have broken through to the surface, making the reality of the disease evident to all but the most deluded of minds. 

What was the Holy Roman Empire?

According to Aristotelian-Thomistic political philosophy, the state is a natural institution.  It has as its natural end the provision of goods that are necessary for our well-being as rational social animals, but would not be otherwise available (such as defense against aggressors).  According to traditional Catholic theology, the state also serves functions relevant to the realization of the supernatural end of salvation, such as protecting the Church. 

However, while these things are true of the institution of the state in general, they do not entail the existence of any particular state.  That is to say, while the natural law and our supernatural end require that there be states, they don’t require that there exists Germany, specifically, or the United States, or China.  For the most part, the same thing is true of empires.  Nothing in natural law or in our supernatural end requires that there be a British Empire, specifically, or a Mongol Empire.

Augustine on divine illumination

Plato held that the Form of the Good makes other Forms intelligible to us in a way comparable to how the sun makes physical objects visible to us.  He also took our knowledge of the Forms to be inexplicable in empirical terms, since the Forms have a necessity, eternity, and perfection that the objects of the senses lack.  His solution was to regard knowledge of the Forms as a kind of recollection of a direct access the soul had to them prior to its entrapment in the body.

Links for Thanksgiving

What the hell happened to the Drudge Report?  The Tablet investigates.

The rediscovery of hell.  At First Things, Cardinal Pell abandons Balthasarian wishful thinking.

Never mind 2020.  David Oderberg asks: How did Donald Trump win in 2016?

Reading Religion reviews Steven Jensen’s book on Thomistic psychology.

The AARP magazine on the heartbreaking last days of Stan Lee. 

Church and Culture radio interview

Last week I was interviewed by Deal Hudson for his show Church and Culture on Ave Maria Radio.  The interview lasts an hour and ranges over my work in general.  You can listen to it here.

You can find links to other radio interviews and the like here.

Tyranny of the sovereign individual

The individual, when isolated, is not self-sufficing; and therefore he is like a part in relation to the whole.  But he who is unable to live in society, or who has no need because he is sufficient for himself, must be either a beast or a god.

Aristotle, Politics, Book I

At The American Conservative, Rod Dreher interviews theologian Carl Trueman about his new book The Rise and Triumph of the Modern Self.  Trueman argues that the collapse of traditional sexual morality cannot be understood except as a consequence of a radically individualist conception of the self that has been working its way ever deeper into every nook and cranny of the Western mind through the course of the modern age – including the minds of many so-called conservatives.  Yet too few defenders of traditional sexual morality realize this.  Trueman says:

Means, motive, and opportunity

Did Joe Biden win the election fair and square?  Or was there voter fraud sufficient to tip it in his direction?  I won’t be addressing those questions here.  I want to consider the more basic epistemological issue of whether asking them is even reasonable, or instead the mere entertaining of a crackpot conspiracy theory.  At The Catholic Thing, philosopher Mike Pakaluk opines that it is reasonable, and two other philosophers, Rob Koons and Daniel Bonevac, evidently agree.  I think they are right.

Trump’s fiercest critics are hardly in any position to disagree.  For years they insisted with shrill confidence that Trump “colluded” with Russia to steal the 2016 election – even though, as honest lefties like Matt Taibbi and Glenn Greenwald vainly tried to warn them, that was a conspiracy theory for which there never was serious evidence.

Pink on Aristotle’s Revenge

In this week’s issue of the Times Literary Supplement, philosopher Thomas Pink kindly reviews my book Aristotle’s Revenge.  From the review:

Edward Feser’s Aristotle’s Revenge is presented as a philosophical defence of Aristotelianism in its robust scholastic form, as exemplified by the work of Thomas Aquinas.  This broadly Thomist Aristotelianism, Feser argues, far from being a block to the study of nature, provides a metaphysics that is the necessary foundation for any science of nature, from physics to psychology.  The “revenge” lies in this fact, and most especially in the indispensability of Aristotelian doctrine to the very understanding of science and scientific investigation itself…

Perfect love casts out fear

Months of lawlessness have left people on edge and anxious, and their anxiety is unlikely to be much abated by the outcome of the election.  For either the party of lawlessness will win, or it will lose and manifest its fury in further rioting, looting, burning, hounding of political enemies, and attempted subversion of lawful authorities.  There remains much to be anxious about either way, and there likely will be for some time. 

“Pastoral” and other weasel words

If names be not correct, language is not in accordance with the truth of things.  If language be not in accordance with the truth of things, affairs cannot be carried on to success.

Analects of Confucius, Book XIII

But let your ‘Yes’ be ‘Yes,’ and your ‘No,’ ‘No.’  For whatever is more than these is from the evil one. 

Matthew 5:37

“Weasel words,” as that expression is usually understood, are words that are deliberately used in a vague or ambiguous way so as to allow the speaker to avoid saying what he really thinks.  The phrase is inspired by the way a weasel can suck out the contents of an egg in a manner that leaves the shell largely intact.  A weasel word is like a hollowed-out egg, one that seems on the surface to have content but which is in fact empty.

Dupré on the ideologizing of science

Philosopher of science John Dupré, like Nancy Cartwright, Paul Feyerabend, and others, has developed powerful and influential criticisms of reductionism.  Whereas Cartwright is best known for her criticisms of reductionism in the context of physics, Dupré has tended to focus instead on biology (though both have addressed the other sciences as well).  Like Cartwright, his style is less mischievous and polemical than Feyerabend’s was.  Dupré’s essay “The Miracle of Monism” is a useful overview of his approach, and contains lessons especially relevant at a time when science (or at least the use to which it is put in public policy) has become ideologized.

Lockdowns versus social justice

The phrase “social justice” has a long and honorable history in Catholic social thought going back to the nineteenth century, but is now typically deployed in defense of policies that are diametrically opposed to social justice as the Church and its thinkers have always understood it.  And unfortunately, this is true even in the case of many Catholics, who lazily adopt various leftist attitudes and policies simply because they are falsely but relentlessly presented as concomitants of “social justice.” 

Last April, Fr. John Naugle argued in an important article at Rorate Caeli that indefinite lockdowns violate the natural human right to labor in order to provide for oneself and one’s family, and thus are deeply contrary to social justice.  He revisits the issue in a follow-up article.  Some Catholic defenders of the lockdowns are people who, in other contexts, claim to stand up for the rights of workers and to oppose consequentialist thinking.  But as Fr. Naugle points out, their rationalizations for the lockdowns are precisely consequentialist in character – pitting the alleged benefits of lockdowns against inviolable natural rights – and harm workers far more than any other segment of society.

The Church embraces Columbus

We saw in a recent post how the Scholastic theologian Bartolomé de Las Casas vigorously defended the rights and dignity of the American Indians against the cruelty of Spanish conquistadors.  Las Casas in no way minimized the extent of this cruelty.  On the contrary, he is commonly accused of exaggeration and overzealousness.  So what did Las Casas think of Columbus?  Did he condemn him as an initiator of oppression?

Joe Biden versus “democratic norms”

No one who claims to favor Biden over Trump on the grounds of protecting “democratic norms” can, at this point, be speaking in good faith.  They are either culpably deceiving themselves or cynically trying to deceive others.  Packing the Supreme Court would be as radical a violation of “democratic norms” as any president has ever attempted.  It would destroy the independence of the judiciary, making of the court a dictatorship for the party in power.  Yet Biden and Harris persistently refuse to say whether they favor court-packing.  Biden has now said that voters “don’t deserve” to know his position on this absolutely crucial issue before the election – even though he acknowledges that “it’s a great question” and says he doesn’t blame people for asking it!  Can you imagine the hysteria that would ensue if Trump gave such a lunatic answer to a question that momentous?  This is reason enough not to vote for Biden, whether or not you vote for Trump. 

Weigel’s terrible arguments

In his article “Truman’s Terrible Choice” at First Things, George Weigel defends the bombings of Hiroshima and Nagasaki.  I respond at Catholic Herald.

Aquinas contra sedition and factional tyranny

As Aquinas teaches, “the chief concern of the ruler of a multitude… is to procure the unity of peace” (De Regno, Book I, Chapter 3).  All other social goods are subordinate to that, because they all presuppose it.  Without peace, no social good is secure.  Without unity – and in particular, without a shared commitment to a common set of laws, procedures, cultural norms, and the like – no peace is possible.

Aquinas contra globalism

In Book Two, Chapter 3 of his little work De Regno (or On Kingship), Thomas Aquinas addresses matters of trade and its effect on the material and spiritual well-being of a nation.  On the one hand, and at the end of the chapter, he allows that:

Trade must not be entirely kept out of a city, since one cannot easily find any place so overflowing with the necessaries of life as not to need some commodities from other parts.  Also, when there is an over-abundance of some commodities in one place, these goods would serve no purpose if they could not be carried elsewhere by professional traders.  Consequently, the perfect city will make a moderate use of merchants.

The rule of lawlessness

As Aristotle and Aquinas teach us, human beings are by nature rational social animals.  Because we are a kind of animal, we need to be safe from violent attack and we need the freedom to acquire food, shelter, clothing and other material goods and to be able to rely on stable possession of them.  Because we are social animals, we need the cooperation of others in order to acquire these material goods, and we also need the warmth of human relationships and a sense of belonging and loyalty to a larger whole – to a family, a community, a nation.  Because we are rational animals, we need for others to appeal to our reason in order to persuade us of their opinions and favored policies, rather than resorting to intimidation and violence.

Scholastics contra racism

Condemning racism (or “racialist prejudice,” as he referred to it), Pope St. Paul VI affirmed that:

The members of mankind share the same basic rights and duties, as well as the same supernatural destiny.  Within a country which belongs to each one, all should be equal before the law, find equal admittance to economic, cultural, civic and social life and benefit from a fair sharing of the nation's riches.  (Octogesima Adveniens 16). 

This suggests a useful definition of racism, which is best understood as the denial of what the pope here affirms.  In other words, racism is the thesis that not all races have the same basic rights and duties and/or supernatural destiny, so that not all races should be equal before the law, find equal admittance to economic, cultural, civic and social life, or benefit from a fair sharing of the nation's riches.

Open thread (and a comment on trolling)

We’re long overdue for another open thread.  Now is the time for you to post that otherwise off-topic comment I’ve had to delete.  From Being Itself to mental health, from Mickey Spillane to John Coltrane, from Dada to Prada, in this post everything is on-topic.  Naturally, the normal rules of decency and civility still apply.

Separating scientism and state

Scientism transforms science into an intolerant and all-encompassing ideology.  Bad as it is when it issues in crackpot philosophy, it can be even worse when used to rationalize destructive public policy – as with the increasingly idiotic and oppressive lockdowns that have been imposed across much of the world.  Now perhaps more than ever we need the corrective provided by the late, great philosopher of science Paul Feyerabend (1924-1994), who argued trenchantly for a separation of scientism and state.  I offer a primer in a new article at The American Mind.